Burger King was not available to comment, while 3i declined to comment when contacted by CNBC.

Burger King, which has a market capitalization of about $2.3 billion, has been public since May 2006.

It had previously been own by private equity, which still holds a stake in the company. TPG, Bain Capital and Goldman Sachshad owned Burger King after buying it from British drinks company Diageoin 2002 for about $1.5 billion.

The Wall Street Journal reported Burger King has been in talks with private equity firms in recent weeks about a possible sale.